Question

Which expressions are equivalent to k^{^{\scriptsize -\dfrac{1}{6}}}k − 6 1 ​ k, start superscript, start superscript, minus, start fraction, 1, divided by, 6, end fraction, end superscript, end superscript ? Choose all answers that apply: Choose all answers that apply: (Choice A) A \sqrt[6]{k^{-1}} 6 k −1 ​ root, start index, 6, end index (Choice B, Checked) B \dfrac{1}{k^6} k 6 1 ​ start fraction, 1, divided by, k, start superscript, 6, end superscript, end fraction (Choice C) C \left(k^{-1}\right)^{^{\scriptsize\dfrac{1}{6}}}(k −1 ) 6 1 ​ left parenthesis, k, start superscript, minus, 1, end superscript, right parenthesis, start superscript, start superscript, start fraction, 1, divided by, 6, end fraction, end superscript, end superscript (Choice D) D

Answer 1

Options

$A)\sqrt[6]{k^{-1}}\\(B)\dfrac{1}{k^6}\\(C)\left(k^{-1}\right)^{^{\scriptsize\dfrac{1}{6}}}$

Answer:

$(A)\sqrt[6]{k^{-1}}\\(C)\left(k^{-1}\right)^{{1/6}}$

Step-by-step explanation:

Given the expression $k^{^{-\dfrac{1}{6}}}$ , we apply the following rule of indices to obtain equivalent forms.

• Negative Exponent Rule: $a^{-m}=\dfrac{1}{a^m}$

• Fractional Exponent Rule:  $a^{1/m}=\sqrt[m]{a}$

Therefore:

$k^{-1/6}=(k^{-1})^{1/6}$

This is Option C,

If we simplify further, we obtain:

$k^{-1/6}=(k^{-1})^{1/6}\\=\sqrt[6]{k^{-1}}$

This is option A.

Therefore, Options A and C are equivalent to the given expression.